So asks Guy Deutscher in a Times Magazine article last year:
The short answer: Yes!
A couple of instances from my own experience of language:
1. Articles: Most languages have them; Latin does not, and this means that in ordinary Latin discourse, the composer can readily overlook distinctions between the definiteness or indefiniteness of a noun. This is important for biblical interpretation in at least one key instance, John 1:1.
In Greek: “ἐν ἀρχῇ ἦν ὁ λόγος καὶ ὁ λόγος ἦν πρὸς τὸν θεόν καὶ θεὸς ἦν ὁ λόγος.” Translating very woodenly: “In the beginning was the word and the word was with the God and god was the word.” The second instance of theos in this passage lacks the article, a fact which gave significant traction to Arian subordinationist exegesis: the word may have been with the one true God, but that same word only was “divine,” theos, rather than ho theos.
The same verse in Latin: “in principio erat Verbum et Verbum erat apud Deum et Deus erat Verbum” (NV). Because Latin lacks the article, this odd feature of the Greek text is lost in translation, making the Latin scripture considerably less amenable to subordinationist readings: here, the one with whom the Word both is with and is is simply “Deus.” (Of course, that’s not to say the Arians were correct — far from it! I just mean to point out one way in which linguistic structures shape the course of higher level discourse.)
2. Gender: the most striking example I’ve come across regarding gender’s effect on language is Hebrew’s delightfully precise assignment to verbs, not merely of person, voice, and aspect, but also of gender. I can’t think of any verses offhand where moving from Hebrew to Greek or Latin introduces grammatical ambiguity, but I’m sure they must be out there.